Math proplem..pls help?

Question

can you please help me with this problem. it's driving me crazy..

a man set aside P480 for a job-training found that the cost was P10 more per day than he expected. so he reduced his training time by 1/2 and thus saved P80. find the length of the training as he originally planned and the expected cost per day.

thank you for helping :)

Answer 1

Let: T = planned length of training, in days

C = expected training cost per day, P/day

t = actual length of training = T/2 days

c = actual training cost per day = C + 10

Eqn1: CT = 480

Eqn2: (C + 10)(T/2) = 480 - 80 or (C + 10)(T/2) = 400

Isolate C in Eqn1:

C = 480/T Eqn3

Substitute Eqn3 into Eqn2, then solve for T:

(C + 10)(T/2) = 400

(480/T + 10)(T/2) = 400

240 + 5T = 400

5T = 400 - 240

5T = 160

T = 32

Substitute to Eqn3, then solve for C:

C = 480/T

C = 480/32

C = 15

Check using Eqn2:

(C + 10)(T/2) = 400

(15 + 10)(32/2) = 400

(25)(16) = 400

400 = 400 Yes!

Therefore, the length of the training as originally planned was 32 days; the expected cost per day was P15/day.